Lowering saddle height

Hi everyone. I recently purchased a GT GTR Series 2 bike. Really great shape but it’s just about 2 -3cm too high for me (beginners mistake). However if can get the seat lower it should be ok. Even with post lowered all the way down it still feels a bit too high.
Are there seat posts that place the seat very close to the seat post? I currently have a Ritchey alloy post and it looks like this.
Are there seat posts that place the seat very close to the seat post? I currently have a Ritchey alloy post and it looks like this.

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Either the bike is too big or your preference is too low.
I am not sure. You have no chance.
This will give you a rough idea
When you stop a bike you come off the saddle standing with one foot planted solidly on the ground, the other on the pedal. Push up back onto the saddle as you move off.
If above method fails and/or frame is touching you when you stand over, then the bike is definitely too big. You’ll only put yourself off cycling if you try to ride that’s the wrong size.
https://wiggle.co.uk/brand-x-inline-6061-seatpost
Seatposts come in different tube diameters, so check before buying.
A lower profile saddle could help too.
It is not just saddle height, if the frame itself is just too big it could effect other aspects of the fit and cause you issues with overall comfort. There is also a safety issue with a big that is too big as you can lack control of the bike (if you have to stop suddenly, can you easily dismount from the bike?).
Can you post a piccie of you sitting on the bike, leg at 6 o,'clock?